I am a physics student. I have a question about this "if you are a mathematics student then it is worthwhile" stuff. Would a great physicist, say like Feynman, know why this is so? Even if your answer is speculative, what do you think?

If the math is a model of some physical situation, you can often argue that derivatives are continuous, etc, on physical grounds. Usually, a math model only hits the "exceptional" conditions that mathematicians like to understand completely, if it's a poor model of the physics.

IMO it is always worthwhile (not to say essential) to know something about the conditions that make your math valid. But as a physicist or engineer you don't necessarily need to know the most general set of conditions that make it valid, or be able to prove why it is valid.

Of course you can never know "too much" math, but in real life, whether you learn more math or more physics is a time management problem.

(Full disclosure: I've seen both sides of this first hand - I have a math degree, and spent most of my life working on engineering problems).